Quantum Trajectories

Principal Investigator

Craig Savage

Department of Physics and Theoretical Physics

This project seeks to understand quantum chaos in
open systems. We use the newly developed method of
quantum trajectories to solve the relevant quantum
mechanical master equations. The broader context of this work is
the investigation of the nature of the interface
between quantum and classical mechanics. Classical
dynamical systems show chaos. We investigate the
corresponding dynamics in quantum systems. A unique feature of
our work is our consideration of open systems, that is
systems interacting with environments. This is significant
because classical systems are typically open. Our immediate
goal is to find a criterion for chaotic dynamics which
is applicable to both classical and quantum systems. To
this end we are investigating an information theoretic
criterion based on the sensitivity of chaotic systems to
perturbations of parameters. The particular dynamical system we
focus on is the second harmonic generator.

Projects

u57-VPP, PC

What are the results to date and the future of the work?

We have published work on the second harmonic generator which establishes a link
between the classical chaotic and quantum mechanical regimes. We now have preliminary evidence
for the validity of an information theoretic criterion for quantum chaos. Our goal is to
firmly establish the validity of this criterion.

What computational techniques are used?

The quantum trajectories code was developed in 1996 by Stuart Midgley as his
theoretical physics honours research project. The quantum trajectories equation is quite similar to
the Schrodinger equation. The code utilises recent algorithmic developments based on
dynamically adapting the quantum mechanical basis to the current system state.